Differential cumulants, hierachical models and monomial ideals

Details Differential cumulants, hierachical models and monomial ideals Differential cumulants, hierachical models and monomial ideals

2011-02-10

arxiv.org/abs/1102.2118v1

Mathematics

Statistics Theory

This work is part of the PhD thesis of Daniel Bruynooghe

Scientific paper

For a joint probability density function f(x) of a random vector X the mixed partial derivatives of log f(x) can be interpreted as limiting cumulants in an infinitesimally small open neighborhood around x. Moreover, setting them to zero everywhere gives independence and conditional independence conditions. The latter conditions can be mapped, using an algebraic differential duality, into monomial ideal conditions. This provides an isomorphism between hierarchical models and monomial ideals. It is thus shown that certain monomial ideals are associated with particular classes of hierarchical models.

Affiliated with

Also associated with

No associations

Rating

Differential cumulants, hierachical models and monomial ideals does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Differential cumulants, hierachical models and monomial ideals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Differential cumulants, hierachical models and monomial ideals will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-694435